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Luden [163]
2 years ago
6

If x=6 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equa

tion?
Mathematics
1 answer:
prisoha [69]2 years ago
8 0
If x=6 is the only intercept, it means that the quadratic is tangential to the x-axis, or equivalently x=6 is a root with multiplicity 2.
The discriminant is typically zero for multiplicity 2 in a quadratic. 
It will be clear looking at the quadratic formula:
if D=b^2-4ac = discriminant of the quadratic, then
x1=(-b+sqrt(D))/2a or x2=(-b-sqrt(D))/2a
if x1=x2 (double root, or multiplicity 2) then clearly D has to be zero.
You might be interested in
A university is applying classification methods in order to identify alumni who may be interested in donating money. The univers
gtnhenbr [62]

Answer:

Accuracy = 0.81

Sensitivity = 0.93

Specificity = 0.81

Precision = 0.047

Step-by-step explanation:

Given the confusion matrix :

Actual_______ Donation___ No Donation

Donation______ 268 (TP) _______ 20 (FN)

No Donation ___5375 (FP) _____23439 (TN)

Accuracy is calculated as :

(TP + TN) / (TP+TN+FP+FN)

(268 + 23439) / (268 + 23439 + 5375 + 20)

ACCURACY = (23707 / 29102) = 0.81

Sensitivity (True positive rate) :

TP ÷ (TP + FN)

268 ÷ (268 + 20)

268 ÷ 288 = 0.93

Specificity (True Negative rate) :

TN ÷ (TN + FP)

23439 ÷ (23439 + 5375)

23439 ÷ 28814

= 0.81

Precision :

TP ÷ (TP + FP)

268 ÷ (268 + 5375)

268 ÷ 5643

= 0.047

4 0
2 years ago
An amusement park's owners are considering extending the weeks of the year that it is opened. The owners would like to survey 10
uranmaximum [27]
The best way to randomly choose the 100 families would be to allow a random number generator to come up with 100 families within a 50 radius of the amusement park.

Using this method would ensure that it is more randomised & not limited to people who come at a specific time or are in a specific area as well as it not be affected by subconscious bias of people when selecting people to survey.
6 0
2 years ago
Read 2 more answers
A certain company's main source of income is a mobile app. The company's annual profit (in millions of dollars) as a function of
liberstina [14]

Answer:

x = $3, or x = $11


Step-by-step explanation:

The equation given is P(x)=-2(x-3)(x-11)

where

  • P(x) is the profit, and
  • x is the app price

<u>We want app prices (x's) when profit (P(x)) is 0, so plugging in into the equation:</u>

P(x)=-2(x-3)(x-11)\\0=-2(x-3)(x-11)\\0=(x-3)(x-11)

<em>It means (x-3) = 0  OR  (x-11) = 0</em>

So, x = 3, or 11

7 0
2 years ago
Read 2 more answers
Line JM intersects line GK at point N. Which statements are true about the figure? Check all that apply.
ki77a [65]
See attached image

First, we must know this: Complementary angles are two angles whose sum is equal to 90°, while supplementary angles are two angles whose sum is equal to 180°. That been said, the only statement which is true is the second statement, <span>MNL is complementary to KNL

Reasons why others are False
</span>GNJ is supplementary to JNK, not complementary
MNG is supplementary to GNJ, not complementary
LNJ (not KNJ) <span>is supplementary to MNL
</span>GNM is equal to JNK, not supplementary

8 0
2 years ago
Read 2 more answers
The Acme Candy Company claims that​ 60% of the jawbreakers it produces weigh more than 0.4 ounces. Suppose that 800 jawbreakers
vichka [17]

Answer:

Yes, it would be statistically significant

Step-by-step explanation:

The information given are;

The percentage of jawbreakers it produces that weigh more than 0.4 ounces = 60%

Number of jawbreakers in the sample, n = 800

The mean proportion of jawbreakers that weigh more than 0.4 = 60% = 0.6 = \mu _ {\hat p} =p

The formula for the standard deviation of a proportion is \sigma  _{\hat p} =\sqrt{\dfrac{p(1-p)}{n} }

Solving for the standard deviation gives;

\sigma  _{\hat p} =\sqrt{\dfrac{0.6 \cdot (1-0.6)}{800} } = 0.0173

Given that the mean proportion is 0.6, the expected value of jawbreakers that weigh more than 0.4  in the sample of 800 = 800*0.6 = 480

For statistical significance the difference from the mean = 2×\sigma _{\hat p} = 2*0.0173 = 0.0346 the equivalent number of Jaw breakers = 800*0.0346 = 27.7

The z-score of 494 jawbreakers is given as follows;

Z=\dfrac{x-\mu _{\hat p} }{\sigma _{\hat p}  }

Z=\dfrac{494-480 }{0.0173  } = 230.94

Therefore, the z-score more than 2 ×\sigma _{\hat p} which is significant.

8 0
2 years ago
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